1. Field of the Invention
The invention relates generally to the detection of weather disturbances and precursors to weather disturbances, and more particularly to the detection of clear air turbulence, microbursts, aircraft wake vortices, gust fronts, thunderstorms, updrafts, downdrafts, convective flows, tornadoes, hurricanes, and cyclones.
2. Description of the Prior Art
Clear air turbulence, microbursts, aircraft wake vortices, gust fronts, thunderstorms, updrafts, downdrafts, and convective flows all present severe hazards to aircraft. Effects on aircraft encountering any of these hazards range from severe buffeting to the ultimate catastrophe. Thunderstorms, tornadoes, hurricanes, and cyclones have been extremely destructive. Though these severe storms may be detected and tracked once they are formed, detecting precursors to their formation have not been implemented. Consequently, warnings of the initial onslaught of these storms cannot be given and loss of life may result at their initiation.
The prior art utilizes two basic techniques to detect hazardous atmospheric flows: Doppler radar and the Radio Acoustic Sounding System (RASS). Doppler radar measures the average radial motion of scatterers in a volume formed by a radar range gate and the antenna beam. Processed samples of the radar return yield the Doppler spectrum of the radar backscatter in each range gate. The zeroth moment of the signal spectrum is a measure of echo strength, the first moment a measure of the mean radial velocity, and the second moment a measure of the Doppler width. Doppler radar backscatter from hydrometeors (rain droplets) and dust are utilized to determine various atmospheric conditions. Doppler radars of the prior art, though useful for the determination of existing weather conditions, are not able to detect the clear air turbulences which are hazardous to aircraft in flight.
RASS emits overlapping radar and acoustic beams from a common ground-based location. Because the air""s index of refraction is a function of density, the acoustic beam, which consists of a spatial pattern of condensations and rarefactions, produces corresponding refractive index variations in situ. Radar waves reflect from these index variations and reflections are strongest when the acoustic wavelength is one-half the radar wavelength. Radar reflections focus onto the radar antenna due to the parallel alignment of the radar and acoustic wavefronts. The Doppler shift of the radar reflections corresponds to the speed of sound.
A vertically pointing RASS has been utilized to measure the vertical temperature profile of the atmosphere by measuring the speed of sound as a function of altitude. Since the speed of sound has a known relation to temperature, a virtual temperature profile of the atmosphere may be deduced from the data. Due to atmospheric attenuation of the sound beam and very small radar reflections from clear air, RASS can measure sound speed, wind velocity, and clear air turbulence only within restricted bounds.
A horizontally pointing RASS has been used to detect, track, and measure the strength of wake vortices of landing aircraft. Segments of the RASS acoustic wave speed up or slow down by varying amounts as they pass through a vortex. As a result, the Doppler spectrum of the acoustically reflected radar signal is a mapping of the vortex""s line-of-sight velocity distribution. Vortex circulation (strength) may be deduced from the Doppler spectrum.
A fluid flow is laminar when the velocity and direction of flow particles do not change with time. Laminar flow is favored by flows with a low Reynolds number, a dimensionless quantity defined as R=LU/xcex3, where L is a characteristic length of the flow, U is a characteristic speed, and xcex3 is the fluid kinematic viscosity. A laminar flow with a high Reynolds number is unstable, so that a slight disturbance changes the flow to turbulent. A turbulent flow consists of overlapping eddies with varying characteristic lengths and velocity scales. First order eddies comparable to the size of the flow appear first. First order eddies generate second order eddies which are smaller and draw their energy from the first. Second order eddies generate third order eddies, and so on, creating a hierarchy of eddies. The smallest eddies have high local velocity gradients which cause them to dissipate under the influence of viscosity and their kinetic energy to be converted into heat.
An eddy may be described as a swirling flow with approximately circular streamlines. Streamline velocities increase linearly from zero at the center to a maximum value, after which they decrease inversely with radius. The eddy core is defined as the region inside the maximum velocity streamline, that fluctuates due to turbulence. Eddy overall size varies from 10 to 30 times the mean core size. FIG. 1A shows the process by which large eddies produce smaller eddies. A kink induced in an eddy""s core by turbulence causes the core to twist into a figure 8. Opposing core flows cause the core to split, culminating in the creation of two eddies with opposite rotation.
Small scale turbulence is essentially homogeneous and isotropic, and may be mathematically described by Fourier eigenfunctions (modes) indexed by wave numbers k, which are related to eddy core size. Mode wave number space may be divided into three ranges, each having its own wave number distribution: (i) low wave numbers (production range); (ii) intermediate wave numbers (inertial range), and (iii) high wave numbers (dissipation range). Eddy wave numbers in the production range are distributed as k4 and in the inertial range as kxe2x88x925/3. Hence, wave numbers on the boundary between the production and inertial ranges have the highest density.
Atmospheric flows typically have high Reynolds numbers and are always turbulent. The size of the largest eddies in the normally turbulent atmosphere are tens of meters while the smallest are several centimeters. Clear Air Turbulence (CAT) refers to a highly turbulent clear air flow that occurs about 10 km above the earth""s surface. Theoretical considerations and observations of the free atmosphere indicate that CAT is mainly a manifestation of stably stratified shear flow instability, generally referred to as Kelvin-Helmholtz instability or KHI. Onset of KHI over an atmospheric layer of depth xcex94z is determined by the layer Richardson number which is inversely proportional to the square of the vector wind change over xcex94z. A necessary condition for KHI is a Richardson number less than 0.25.
CAT turbulence is severe enough to perturb the motion of aircraft flying through it, causing injuries to passengers and cabin attendants as well as structural damage to aircraft. CAT can be neither seen nor avoided by pilots without prior knowledge of its location. The largest eddies in CAT may be several kilometers, corresponding to the flow size. Flow velocities typically range from 100 to 200 kts (50 to 100 m/s).
The two well-known mechanisms by which kinetic energy is converted into sound are, first, by forcing a mass in a fixed region of space to fluctuate, as with a loudspeaker diaphragm embedded in a very large baffle, and second, by forcing momentum in a fixed region of space to fluctuate, which occurs when a solid object vibrates after being struck. The first is more efficient than the second.
Localized fluctuations in turbulent flows produce pressure variations that propagate away from their source and, if an observer is present, will be recognized as sound. Examples include the roar produced by high winds, the noise emitted by jet aircraft exhaust flows, and the whooshing sound produced by aircraft wake vortices. The mechanism by which sound is generated aerodynamically is fundamental because fluctuating shearing motions are converted into fluctuating longitudinal motions. The conversion efficiency is much smaller than either of the above mechanisms.
It has been shown that there is an exact mathematical analogy between density fluctuations in a turbulent flow and density fluctuations produced by fluctuating quadrupoles in a non-moving medium. A quadrupole consists of two correlated, opposite polarity, dipoles whose axes are aligned in one direction and whose physical positions may be aligned in another. A quadrupole is longitudinal when the two directions coincide and lateral when perpendicular. Every quadrupole can be described in terms of longitudinal and lateral quadrupoles.
It has been further shown that quadrupoles radiate sound because density fluctuations generated by a quadrupole""s constituent dipoles do not arrive simultaneously in the far field. Stated mathematically, quadrupole sound radiation is due to the rate of change of dipole strength at a point in the far field even though total dipole strength in the near field is zero at any instant. Referring again to FIG. 1A, it may be seen that the newly split core constitutes two dipoles with opposite polarities, i.e. a quadrupole. Thus, the same mechanism that splits an eddy core simultaneously creates a quadrupole that radiates sound until the constituent dipoles decorrelate.
Flow generated sound power Fs radiating through a surface of dimension l2 may be represented by (Fs=xcfx81xcexd8xcexdsxe2x88x925l2), where xcfx81 is the medium density, xcexd is the flow velocity, and xcexds is the speed of sound. Since flow kinetic energy Fk entering a region is given by (Fk=xcfx81xcexd3l2), the sound conversion efficiency is proportional to M5, where (M=xcexd/xcexds) is the flow Mach number. Conversion efficiency at low Mach numbers is exceptionally small, resulting in very little radiated sound.
Flow transport modifies a quadrupole""s radiation pattern only for significant flow Mach numbers. For example, in a Mach 0.2 flow, a longitudinal quadrupole""s sound intensity increases slowly from 0 dB at 90 degrees (relative to the flow) to +5 dB at 0 degrees; and decreases from 0 dB at 90 degrees to xe2x88x923 dB at 180 degrees. In the case of lateral quadrupoles, sound radiated at 135 degrees is the 0 dB reference. Between 0 and 90 degrees, directionality is similar to a positive half sine wave with a peak value of 4 dB near 40 degrees. Between 90 and 180 degrees the curve shape is also similar to a half sine wave with a peak of xe2x88x922 dB near 130 degrees. There are sharp nulls at 0, 90, and 180 degrees. For lower Mach number flows, the radiation pattern is essentially non-directional, especially since quadrupoles not only have random orientations but radiated waves are also randomly refracted passing through adjacent large eddies.
Numerous laboratory measurements of sound produced by small jets confirm the above. FIG. 1B shows radiated spectra for various jet diameters and velocities as a function of the product (fD/UJ), sometimes known as the Strouhal number, where f is the radiated acoustic frequency, D is flow size, and UJ is flow velocity. In this figure, spectral curves from different sources were slightly shifted to the left or right to make all spectral peaks occur at a Strouhal number of one. It may be noted that spectral shapes are essentially the same for widely different flows, suggesting that FIG. 1B also applies to sound spectra radiated by atmospheric flows.
The shape of the normalized spectrum may be explained as follows. At Strouhal numbers less than one, the radiated intensity varies as the fourth power of frequency due to the Stokes effect. At Strouhal numbers greater than one, the radiated power depends on quadrupole spatial density in the inertial range so that intensity decreases at 5 dB/octave (5/3xc3x9710 log 2).
FIG. 1C shows spectra radiated by a 25 mm jet for three jet velocities in an anechoic chamber. The peak frequency radiated by a 125 m/s (250 kt) jet is about 4.5 kHz. This contrasts with a peak frequency of 78 Hz generated by a 35 kt wind measured at the top of Mount Washington (NH). The measured wind spectrum was also found to decay at 5 dB/octave above the peak.
The boundary between the inertial range and the dissipation range is often referred to as the microscale. Quadrupole sizes near the microscale radiate the highest frequencies. In the normally turbulent atmosphere the radiated spectrum extends to roughly 10 kHz. Since the microscale decreases with increasing turbulence, CAT sound spectra are expected to extend to above 30 kHz.
The lifetimes (correlation times) of quadrupole radiation may be deduced from the characteristic time scale T≈L/U, of a turbulent flow, where L and U are characteristic length and velocity scales of the flow. Since CAT flow sizes are of the order of a kilometer and flow velocities of the order of 50-100 m/s, the flow time scale, and therefore also the lifetime of the largest quadrupoles, is about 10 seconds. Assuming characteristic time scales of small scale CAT turbulence to be two orders of magnitude lower, the lifetime of the smallest quadrupoles (highest frequencies) is around a tenth of a second. Near the earth""s surface, the smallest eddies are several times larger than those in CAT, resulting in quadrupole lifetimes of the order of several tenths of a second.
In a fully turbulent flow, first order eddies approximately fill the flow volume without overlap. Because eddies in the production range are distributed as the fourth power of eddy size, higher order eddies increasingly overlap until the boundary between the production and inertial ranges is reached, after which eddy size density decreases. Assuming a first order CAT eddy size of 4800 m and a most populous CAT eddy size of 1200 m (with a 60 m core that produces a peak radiated frequency of 5 Hz), the number of overlapping 1200 m eddies is about 256. Hence, 4.7 m eddies (1200 m/256) fill the volume without overlap. Assuming a 4.7 m eddy core size of 0.16 m, the spatial density of 0.16 m eddy cores relative to 1.5 cm cores (corresponding to a radiated frequency of 20 kHz) is about 3.7 so that the average spacing between 1.5 cm quadrupoles is approximately 17 m.
As stated above, existing radar techniques for detecting hazardous atmospheric flows and precursor flows require embedded hydrometeors and/or dust to generate a detectable radar return. It is desirable to detect and measure the velocity and turbulence of clear air flows remotely, as well as those containing embedded hydrometeors and/or dust, which not only fills a void in present capabilities, but also permits early detection of clear air flows that are precursors to many hazardous weather disturbances.
It is the objective of the present invention to detect and measure the velocity and turbulence of hazardous atmospheric flows including CAT, microbursts, aircraft wake vortices, gust fronts, thunderstorms, updrafts, downdrafts, convective flows, tornadoes, hurricanes, and cyclones using ground, airborne, and space-based means.
An object of the invention is to detect CAT from onboard an aircraft in flight.
Another object of the invention is to detect microburst downflows and outflows (including dry microbursts) at airports using ground and onboard aircraft means.
A further object of the invention is to detect, track, and measure aircraft wake vortices at airports.
A still further objective of the invention is to eliminate radar ambiguity in the measurement of hazardous wind velocities by Doppler weather radar.
A still further object of the invention is to detect atmospheric flows relating to thunderstorms, tornados, hurricanes, and cyclones.
All of the above objects are achieved by the measurement of the Doppler shift and Doppler width of radar signals reflected from refractive index variations produced by sound waves generated within atmospheric flows. For reflection to occur, the sound wavefronts must be parallel to the radar wavefronts and also satisfy the Bragg condition. Since aerodynamically generated sound has a wide spectrum and is essentially non-directional, radar wavefronts across the entire radar beam are reflected towards the radar. This is true for acoustic waves traveling towards as well as away from the radar.